Let $$(a_n)_{n=0}^{\infty}$$ and $$(b_n)_{n=0}^{\infty}$$ be two sequences and let $$\varepsilon > 0$$ be a rational. $$(a_n)_{n=0}^{\infty}$$ is said to be ε-close to $$(b_n)_{n=0}^{\infty}$$ iff [...] for all $$k \ge 0$$.